AP STATISTICSChapter 10 Review
1. A news service reported the average number of violent acts per hour of television for each of the following networks.
Network / Mean number of Violent Acts per HourABC / 15.6
CBS / 11.9
FOX / 11.7
NBC / 11.0
Suppose each of these means was computed on the basis of viewing n = 50 randomly selected prime-time hours and the population standard deviation, , is 5. Find a 90% confidence interval for , the true mean number of violent acts per prime-time hour for ABC.
This is a z-interval for means, and the variable of interest is the number of violent acts per prime-time hour on ABC network.
We are given a large 50>30 random sample, so the sampling distribution is approximately normal.
We are 90% confident that the true mean number of violent acts per prime-time hour on ABC network. In repeated random sampling, this method successfully captures the true mean 90% of the time.
2. The level of calcium in the blood of healthy young adults follows a normal distribution with mean µ = 10 milligrams per deciliter and standard deviation milligrams per deciliter. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is = 9.85. Is this evidence that the mean calcium level in the clinic population is less than 10? Carry out a complete statistical analysis of this question.
We are uncertain of having an SRS. The sample size is large, 100>30, so the sampling distribution is approximately normal, by CLT.
Reject H0, a test statistic this small will occur by chance alone less than 5% of the time. (.048<.05) We have strong evidence that the true mean calcium level in healthy pregnant young women is less than 10 mg/dl, the mean for healthy young adults in general.
3. The time needed for college students to complete a certain paper and pencil maze follows a normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean reaction time µ is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. You compute the average of their times to complete the maze and will use this information to test this hypothesis at the level.
a)What is the probability of Type II error when the true mean is 27 seconds?
Find the that corresponds to . on the left and
on the right
We will reject H0 whenever . We will then fail to reject H0 when . When , . This is found by
Even a small difference, such as using 28, instead of 28.04, changes the result:
b)What is the approximate power of your test at µ = 27 seconds?
4. The price to earnings ratio (P/E) is an important tool in financial work. Generally, a low P/E ratio indicates a better value or bargain stock. A random sample of Southeastern banks gave the P/E ratios given in the table. Yahoo Finance recently reported the mean P/E ratio for the entire banking sector to be 19. We assume that for the banking sector P/E ratios. Do these data indicate that Southeastern banks have a lower P/E ratio than doesthe banking sector as a whole?
3.96 / 11.88 / 16.59 / 20.908.47 / 13.23 / 17.19 / 23.48
9.66 / 15.23 / 18.06 / 25.20
10.95 / 16.02 / 20.59
μ is the true mean P/E ratio for Southeastern banks.
The sample is reported to be random. The normal probability plot is approximately linear, consistent with a normal model.
Reject H0, a test statistic this small will rarely occur by chance alone.
We have strong evidence that the true mean P/E ratio is less than 19, the mean for the banking sector as a whole.